Capturing, Modeling, Rendering 3D Structures

1. Capturing, Modeling, Rendering 3D Structures Omnidirectional Cameras

2. Cameras • Traditional camera • Pinhole Camera Model • Problems: aberrations, distortions • Tradeoff between aperture, shutter speed, focus, dynamic range • Calibration • Fit an assumed camera model to an actual camera • Omnidirectional cameras • Single camera, multiple cameras, etc • Localization and pose estimation • Where is the camera relative to the object or environment

3. A little bit of history… • Omnidirectional cameras are also called panoramic cameras • “Panorama” comes from the Greek phrase “all sight” • Originally used for artistic purposes • Robert Barker obtained a patent for the idea of a panorama in 1794 • “A Painting without Equal” • In 1800s, panorama became a common European word

4. A little bit of Biology… • Some animals are capable of panoramic vision • e.g., certain insects, crustaceans (e.g., lobster) • Diurnal Insect Vision • Nocturnal Insect Vision • Crustacean Vision

5. Taxonomy of Omnidirectional Camera Designs • Single center-of-projection • Like a traditional camera, light rays meet at a single “focal point” • Multiple center-of-projection • Camera does not have a single focal point • Sampled surfaces can be missing or duplicated in full image • Mathematical (re)projections are more complicated • Single Camera/Image • One “view” is acquired per image • Multiple Camera/Image • A single “view” composed by compositing several images

6. Example Omnidirectional Camera Designs • Rotating camera design • Fish-eye lens design • Multiple camera planar mirror design • Single camera curved mirror design

7. Rotating Camera Design • Place a camera on a tripod and spin it around snapping pictures every so often • Pros • Simple • Cons • Multiple centers-of-projection • Multiple (overlapping images) to composite • Vertical “jitter” • Slow acquisition process

8. Rotating Camera Design original warped “stitched”

9. Fish-Eye Lens Design • Use a wide field-of-view lens (~180 degrees) placed in front of a traditional camera • Pros: • Also relatively simple for users (making the lens can be troublesome for designers) • Cons: • Very severe image distortion • Low resolution around perimeter of field-of-view • Almost a single center-of-projection

10. Multiple Camera Planar Mirror Design • Catadioptric = reflective (mirror) + refractive (lens) • http://www.fullview.com [Nalwa96]

11. Single Camera Curved Mirror Design • Theoretical solutions to a single center-of-projection panoramic camera use mirrors that are subsets of swept conic sections • Cones • Spheres • Ellipsoids • Hyperboloids • Paraboloids

12. Single Camera Curved Mirror Design • Theoretical solutions to a single center-of-projection panoramic camera use mirrors that are subsets of swept conic sections • Cones • Spheres • Ellipsoids • Hyperboloids • Paraboloids

13. Conical Mirror

14. Spherical Mirror

15. Ellipsoidal Mirror

16. Hyperboloidal Mirror

17. Paraboloidal Mirror

18. Catadioptric Paraboloidal Camera Motorized cart with camera, computer, battery, radio remote control [Aliaga01,02] Design by [Nayar97]

19. Catadioptric Paraboloidal Camera z x focal point reference plane m mirror p image plane i Theoretical camera model

20. Catadioptric Paraboloidal Camera reference plane m mirror ^ n p H lens image plane i Practical camera model [Aliaga01]

21. - - ˆ ˆ n i m n p m × × = - - ˆ ˆ n i m n p m Catadioptric Paraboloidal Camera Calibration • Assuming incident equals reflected angle: • And given a 3D point p, mirror radius r, convergence distance H, we group and rewrite in terms of mr: mr5-prmr4+2r2mr3+(2prrH-2r2pr)mr2+ (r4-4r2pzH)mr-(r4pr+2r3Hpr) = 0

22. Omnidirectional Vision Home Page • http://www.cis.upenn.edu/~kostas/omni.html